In wireless communications, superheterodyne radio receivers use a mixer to bring the radio frequency (RF) signal down to an intermediate frequency (IF) which can be processed more easily. The IF signal is then demodulated to extract baseband data. When digital demodulation is used in superheterodyne radio receivers, the IF analog signal is converted to digital form using an analog-to-digital converter (ADC) at an ADC sampling rate fadc. An advantage of selecting the intermediate frequency (IF) to correspond to fadc/4 is that sine and cosine waves used for quadrature demodulation of the ADC output can be represented digitally using only 1, 0, and −1, as shown in the following equations.
            cos      ⁡              (                  2          ⁢          π          ⁢                                          ⁢                      f            IF                    ⁢          t                )              =                  cos        ⁡                  (                      2            ⁢            π            ⁢                                                  ⁢                                          f                adc                            4                        ⁢            t                    )                    =                        cos          ⁡                      (                          2              ⁢              π              ⁢                                                          ⁢                                                f                  adc                                4                            ⁢                              (                                  nT                  s                                )                                      )                          =                              cos            ⁡                          (                                                                    2                    ⁢                    π                                    4                                ⁢                                  1                                      T                    s                                                  ⁢                                  (                                      nT                    s                                    )                                            )                                =                                    cos              ⁡                              (                                                      π                    2                                    ×                  n                                )                                      =                          {                              1                ,                0                ,                                  -                  1                                ,                0                ,                1                ,                …                            ⁢                                                          }                                                      sin      ⁡              (                  2          ⁢          π          ⁢                                          ⁢                      f            IF                    ⁢          t                )              =                  sin        ⁡                  (                      2            ⁢            π            ⁢                                                  ⁢                                          f                adc                            4                        ⁢            t                    )                    =                        sin          ⁡                      (                          2              ⁢              π              ⁢                                                          ⁢                                                f                  adc                                4                            ⁢                              (                                  nT                  s                                )                                      )                          =                              sin            ⁡                          (                                                                    2                    ⁢                    π                                    4                                ⁢                                  1                                      T                    s                                                  ⁢                                  (                                      nT                    s                                    )                                            )                                =                                    sin              ⁡                              (                                                      π                    2                                    ×                  n                                )                                      =                          {                              0                ,                1                ,                0                ,                                  -                  1                                ,                0                ,                …                            ⁢                                                          }                                          where:fadc is the analog-to-digital converter sampling frequency,fIF is the intermediate frequency (fIF=fadc/4),TS is the analog-to-digital converter sampling period (TS=1/fadc),t is the time in the analog domain,n is the sample index of the sine and cosine waves in the digital domain.
A superheterodyne receiver with its intermediate frequency set to fadc/4 requires an extra decimate-by-two function after the digital low-pass filter in order to reduce the sample rate so that the signal spectrum is properly represented using the smallest possible sample rate.
According to the Nyquist sampling theorem, the frequency of the analog-to-digital converter must be chosen so that fadc/2 is larger than the bandwidth B of the received signal:
            f      adc        2    >      B    .  
In some radio communication systems, the received signal bandwidth B can be very large, which may impose a large sample rate fadc. Some large sample rates fadc cannot be realized using the existing hardware technologies such ASICs and FPGAs. One approach to address this problem is to duplicate the hardware and operate the two sets of hardware at half the rate in order to achieve the prescribed sample rate. But undesirable tradeoffs with this approach include increased cost, complexity, power consumption, and circuit area. A more optimal approach is desired that allows superheterodyne radio receivers to receive signals with high bandwidths but without one or more of these undesirable tradeoffs or with one or more of these undesirable tradeoffs at least significantly reduced.